Average Position Measurement

When the multibunch signal reaches a steady state, a phase advance is seen every sample that is proportional to the bunch separation. The RF frequency is always therefore, seen as an exact multiple of 1.5 GHz, the nearest of which is 15 GHz. During the steady state period, regardless of the radio frequency, the downmixed signal is therefore at 200 MHz and is stable in phase. The amplitude and phase of the DDC signal, as used for the processing are shown below:

The resolution achieved by averaging over these samples after normalisation versus the bunch to bunch position jitter is shown below. This was calculated from the the average determined by the processing minus the average position of the bunch train.

Single Train Measurement

Making use of the effect seen in simulation, a new simple algorithm was designed using digitally down converted signals whose amplitudes were summed and whose phases were sampled at a single point. In terms of digitiser resolution, the result is similar to with the averaged normalised samples. The digitiser floor is slightly higher here (180 nm) because the cavity is detuned by 10 MHz.

The algorithm described above does not work so well in the case where the phase is changing a lot close to the center of the BPM. A better algorithm sums the whole ddc waveform and takes the phase and amplitude of the result. This algorithm is also insensitive to jitter as the one above.